Fitting the data

The reconstruction and the fitting parts are totally independent.

The fitting functions expect a multidimensionnal-array with the echoes along the last dimension. The images should not be in complex, remember to use abs.(img).

Exponential $T_2$ fitting + noise

In the publication we used an analytical model to fit the exponential decay of the echoes :

\[S(t) = \sqrt{\left(M_0 \ exp(-\frac{t}{T_2})\right)^2 + 2 \ L \ \sigma_g^2}\]

where L is the number of coil and $\sigma_g$ corresponds to the gaussian noise level on the image.

You can perform this fit with the following function :

Subspace_MESE.T2Fit_exp_noise — Function
    T2Fit_exp_noise(ima::Array{T,N}, t::AbstractVector{T}; removePoint::Bool=true, L::Int=1, mask = nothing) where {T<:Real,N}

Fit the relaxation parameters T2 with the equation : $S(t) = \sqrt{(M_0 \exp(-\frac{t}{T2}))^2 + 2 L \sigma_g^2}$ where L est le nombre de canaux, et $\sigma_g$ le bruit gaussien sur les image

Arguments

  • ima::Array{T,N}: multi-dimensionnal images. Last dimension stores the temporal dimension
  • t::AbstractVector{<:Real}: times vector in ms
  • p0=nothing: starting values for fit, if empty p0=[maximum(ima),30,maximum(ima)*0.1]

Keywords

  • removePoint::Bool=true: remove the first point before fitting
  • L::Int=1: Number of coil elements
  • mask::

Returns

  • fit_params : parameter maps last dimension stores the following maps (M₀ , T₂ , σ)

Bibliography

  • Cárdenas-Blanco A, Tejos C, Irarrazaval P, Cameron I. Noise in magnitude magnetic

resonance images. Concepts Magn Reson Part A [Internet]. 2008 Nov;32A(6):409?16. Available from: http://doi.wiley.com/10.1002/cmr.a.20124

  • Feng Y, He T, Gatehouse PD, Li X, Harith Alam M, Pennell DJ, et al. Improved MRI R 2 *

relaxometry of iron-loaded liver with noise correction. Magn Reson Med [Internet]. 2013 Dec;70(6):1765?74. Available from: http://doi.wiley.com/10.1002/mrm.24607

source

The keyword removePoint can be used to delete the first point in the TE vector as well as the first temporal volume in order to reduce the sensitivity of the fit to the stimulated echo.

EPG $T_2$ fitting + noise (WIP)

Another possibility is to fit the equation with an EPG model that, in addition to $M_0$/$T_2$/$\sigma$, also fits the $B_1$ field.

With the current implementation, the fit is not robust enough and also takes too long to use on a 3D volume.

T2Fit_epg_noise